On the automorphism groups of some AG-codes based on $C_{a,b}$ curves

Abstract

We study $C_{a,b}$ curves and their applications to coding theory. Recently, Joyner and Ksir have suggested a decoding algorithm based on the automorphisms of the code. We show how $C_{a,b}$ curves can be used to construct MDS codes and focus on some $C_{a,b}$ curves with extra automorphisms, namely $y^3=x^4+1,y^3=x^4-x,y^3-y=x^4$. The automorphism groups of such codes are determined in most characteristics.

A recent update of an old paper from 2006. Some connections to superelliptic curves are explored and references updated

References in corpus (4)

• Determining equations of families of cyclic curves
• Thetanulls of cyclic curves of small genus
• On Jacobians of curves with superelliptic components
• Subvarieties of the hyperelliptic moduli determined by group actions

Cited by in corpus (1)

• Determining equations of families of cyclic curves